I'd like to add a door into the entrance of a passageway which leads into the bedrooms. The entrance dimensions are 87 1/4 X 39 3/4 and is drywall. it seems the standard door widths are 36 X 80, so it seems I will need to add a frame. I've looked at some doors and the "assembled" height/width seems to be 1.75 inches over the doors widths - what does this mean? What would be the best method of building a frame to support a door on this size, especially the top as I have just over 6 inches I'll need to build up. What would the internal dimensions need to be to support a door 36 X 80?
The recommended rough opening for a 36" x 80" door, is 38 1/2" x 82". So you're basically looking at something like this.
Basically, you'll have to fill the purple area with framing. Which means you might have to either use thin planks on the sides, or cut into the walls to install framing.
The rough opening (blue) around the jamb (brown) will be left open, and shims will be used to make sure the jamb is perfectly level and plumb. This area will be covered by the casing, once the door is trimmed out.
Finally the door (green) will be fitted within the jamb.
The 1 3/4" you're seeing as "assembled" dimensions, includes the door, the small gap between the door and the jamb (3/16"), and the jamb itself (11/16"). This is typical of prehung doors.
Note: Just to confirm my answer below. You could frame it in the current wall if the wall is not load bearing. Since this is on a corner we could not install pocket doors unless it was a non load-bearing wall. If you tried it would sag an door would close right. Also in the OP's situation it would not meet code in an part of the US to install any type of door next to steps.
I am not sure what your exact situation is but I did something very similar in my last house. We had a hallway that led to 4 bedrooms. The kitchen was right by the entrance to the hallway so it became very noisy.
Again I was right around the same dimensions as you too - think mine was about 38" wide.
What I did was install a pocket door. These come in practically any size and I remember getting a 40". In my situation I had to cut out part of my wall, create a header going across, cut out a super small section of the other side to place end of header with support blocking, and some minor drywall repair. It took a few hours total to install door. Another couple to do finish work.
On the side that the door hits I installed two pieces of trim that went to door top trim. Door went inside trim pieces. So I lost less than a half inch of hallway width. I did lose about 6 inches of hallway height - just at the entrance.
Reason why I mention the pocket door scheme is because hallways are open for a reason. You need to get furniture through. If you create another smaller door you might have trouble getting stuff in. I know when I sold my house most people didn't even notice the pocket door until we showed them and then it was them playing with it telling me it was cool. If you post some pictures I can give you an idea on how it would be framed.